What I would argue is the TNG characters connected to the audience where when things people consider dumb happened (e.g., Borg DNA, long lost unknown family, etc.) the characterizations were able to pull the audience through that because they gave a shit what happened to these people. They cared about Riker's and Troi's relationship. They cared about Picard's connection to Jack. They cared about Data's future and for frickin' Spot.
Was there really much investment in Picard's relationship with Jack? The interest seemed to be almost exclusively the return of TNG elements. Jack was, in many ways, simply a walking mystery box. His lack of appeal would, I suspect, be very quickly revealed if he was to have a lead role in a new show.
As for the greater connection with the characters, I'd suggest that is more to do with familiarity and nostalgia than a difference in the quality of character writing. Troi in particular was notoriously regarded as a badly-written character. Behr and Moore spoke openly about how much they disliked writing TNG characters, being bound to do so in such bland and artificial ways.
Much of the fanbase grew up with these characters, and have seen them in 170-odd episodes many times over. Of course there will be greater investment for many such fans in them than new characters which have only been seen more recently in far fewer episodes.